Question

From parallax method the sun is found to be at a distance of about 400 times the earth-moon distance. Estimate the ratio of sun-earth diameters. (diameter of earth = 4 times the diameter of moon)

Answer 1

Given :

The ratio of distance of earth and moon from the sun = 400:1

To Find :

The ratio of sun-earth diameters

Solution :

• As seen from the earth both the sun and the moon appear to be of same angular diameter

• The angular diameter is given by the relation

            $\theta=\frac{D_{sun} }{D_{sun} } = \frac{D_{moon} }{D_{moon} }$      

            $400=\frac{D_{sun} }{D_{sun} } = \frac{D_{moon} }{D_{moon} }\rightarrow Equation(1)$

• we know that

             $\frac{D_{earth} }{D_{moon} } =4\rightarrow Equation(2)$

• By dividing equations 1 & 2 we get

             $\frac{D_{sun} }{D_{earth} } = \frac{400}{4} =100$

The ratio of diameters of sun & earth is 100:1            

           

Answer 2

Given :

The ratio of distance of earth and moon from the sun = 400:1

To Find :

The ratio of sun-earth diameters

Solution :

As seen from the earth both the sun and the moon appear to be of same angular diameter

The angular diameter is given by the relation

                 

           

we know that

             

By dividing equations 1 & 2 we get

             

The ratio of diameters of sun & earth is 100:1